ELECTROMAGNETIC ENERGY DENSITY AROUND A SUPERCONDUCTING COSMIC-STRING

The electromagnetic energy density w(r) is calculated outside an infinitely long and straight superconducting cosmic string of finite radius a. The feature distinguishing this situation from the analogous situation in Minkowski space is the presence of the factor (1-4 G mu)(2) in the azimuthal part of the line element, G being the gravitational constant and mu the string mass per unit length. We regularize w(r) by subtracting (i) one volume term arising from the (boundary independent) volume terms in the two scalar Green's functions, and (ii) one term giving the energy density for the same geometrical configuration but with the gravitational field switched off The remaining regularized energy density w(reg)(r) is calculated and illustrated graphically. The expression is finite everywhere for r > a, but diverges near the surface as (r-a)(-3). This is the typical kind of divergence encountered for the electromagnetic field near a curved boundary even in Minkowski space. The physical reason for this divergence is the assumed idealized boundary conditions at the surface.